AS FOR DOWNLOADING THE MUSIC:
On the webpage in question, in the Download/Music section, it is stated outright: "The translator has given permission to host the files here." Therefore it is safe to download these music pieces, even if the translator has not given such permission. Why? Because to Your best knowledge, without You having to do excessive work, You've been told that this source is legal, and it is now the webpage admin's liability, not Yours.
Of course, if You wish, You could contact Pixel directly and ask them about the site to verify its truthfulness. It's up to You as to how much work You'd be willing to put into this "finding out". In my opinion, You are in the clear - to the best of my knowledge.
(it might be good to save a copy of this Download page in order to show that You were in fact given permission from a person that appeared to be within their rights to give such permission)
Please note that You're only allowed to download and use these files for Your own uses. Any further distribution on Your part (except where permitted by the so-called Fair Use clauses) would constitute breaking the law.
AS FOR MAKING THE VIDEOS:
It depends on what You're trying to make. If You're using the music to critique, show a portion of the game, for review purposes and similar, then Your use would be governed by the Fair Use clauses. In most other cases it is illegal to mix such music with Your own works of art - creating a so-called "derivative work". A good rule of thumb for determining if something is a "derivative work" would be - if the copyrighted content were unavailable/not included in the work, would it still be a work of art on its own? If not, then it's a derivative work.
Again, keep in mind that You're pretty much free to do whatever pleases You with this downloaded music, as long as You don't show it to other people (which would constitute distributing). While it's technically illegal to even create derivative works (unless permitted), no-one can really put You in prison for making a video for Your own, private amusement.
(did I mention that copyright cases are never really as clear-cut as the recording industry is trying to make them?)
BUT - there IS a light at the end of the tunnel! Apparently the distributor (Pixel?) is willing to work with fans of the game(s), even allowing the music to be downloaded from a small webpage (not owned by them) dedicated to the game(s). In this case - You could contact them directly and simply ask for permission to use the music in Your video clips! There's a pretty good chance they'll say 'YES', as long as You make it non-commercial.
And just for the record, even if the music WERE available via iTunes, You still would have to ask for permission to use it in Your own creations.
----------------------------------
The question of legality doesn't have much to do with iTunes. There is no one simple answer.
The more important problem of "legality" doesn't involve downloading, but distributing = sharing, giving. In most cases, the person doing the sharing (distributing) would be liable if they don't have the proper authority (in the form of a license) to do so. Why this problem crops up in 'downloading' is mainly to do with Peer-to-Peer networks (like BitTorrent) which also share (distribute) the content while downloading it (it's how the network works). In general You can't be held liable for downloading, but You can be held liable for making available to others (without permission).
Once again, HTTP (WWW) downloads from web pages are safe in that You only download, and not share/distribute anything in the process. In any case, as stated above, the web page in question seems to have permission for distribution, so it's safe for You to download these files.